Question

study the converges unformly ?

* au f (x) x W xE68] study the roaware unformlyz Pux). aut tx Głos) * fn U l = X en Neolus)

please provide detailed step by step solution

Real analysis

Question in Real analysis

Answer 1

n-> #n>NEN Dhene eso řs arbitary tue fon). 3 ffx) = x21 n6 [,87 . How lim fn(x) = lim n = 0 = f(x) The point wise limit of face) is on Now Iffel - flus / <& fn(2) fin) point wise) ' że find is point wige limit of real no .. aweo I forn) - HW I = 192-01 - lle - ce + x² <n but at [0 18] - 1x21 = 16 a 16 an n does not depends on a , de [0, 8] ..s lin (n) - fins <e & ns Is e nen) Hence fn (n) is uniforenly converegent on xeło, 87 to f(M)=0 ② h (n) = end, &x600, 3] The point-wire limit of fn (n) is given by ncing o e-hø e -0 =f(n) a fin)=0 is the point wise limit of fuld), il for eso, I meen such that (fo(n) - tons ice , & ns Abg IEN alowe lfoen)-f(n) 1 = le-hw.olclethal<e > Hulee - enoru ce in ce = Leen on an> ln (V) => ny 7 in Lv an does not depends on x in to, 39 cs ielfalender fin) ) < *ng y ln (Ve), nen pencens in one's Uniformly convergesst ten all reto 33 to fem)=0 enn

© , x) = xe-n* 4- x = lẽ, 8 Point wise limit of frin) is given by lingo hen) = nuimme on = 0 = fen). a fon Exo, MEN sit [fn (s)-f(n)) ce & nona en Now (frems – tcw) = ( x -0 = Tekird ze le tel ZE - CE - žen (4€ 798) => 1013) ore an> n (%) (n> 3 in (3) Alfnen) - finsj ce & no z ln (36) ) DEN = n does not depends on se, hence by the definition of aniforem convergence finch) fino uniforemily že fn (n) is uniformly convergent on 29,3). Scanned with CamScanner